What is a singularity? In mathematics, a singularity is a place where something blows up --- where a function goes to infinity or otherwise has perverse, degenerate behavior. For instance, the simple function 1/x clearly gets into trouble as x goes toward zero from either side. And there are even more bizarre examples, such as functions that oscillate faster and faster as one approaches a point, with the speed of vibration going to infinity even though the function itself remains finite there. (Try evaluating sin(1/x) with a calculator for small values of x.)

Singularities are fun because they stress our prejudices, which we've built up from experience in non-singular environments. Singularities are also important, in that they can encapsulate information and sometimes control the behavior of functions far away, as an anchor can control a ship. Physics encounters singularities in idealized cases such as a point-like electrical charge (which would seem to have infinite electromagnetic field energy and therefore infinite mass) or the ultimate gravitational collapse of a black hole. Singularities in physics are a vital symbol of our ignorance --- since they indicate a breakdown of known physical laws.

In human events, there are fascinating circumstances where societies go through (or near) singularities --- abrupt catastrophic changes that don't connect smoothly with the past. Examples include revolutions, monetary collapse, and mass migrations. Some historical instances of this sort of thing are described in Extraordinary Popular Delusions and the Madness of Crowds ... the Crusades, the Tulip Mania and other stock market "bubbles", the Witch Burnings, the spread of catch-phrases in language, etc. Vernor Vinge in various of his stories (The Peace War, Marooned in Realtime, ...) and essays has wrestled with the possibility of a social singularity affecting all of humanity. He envisions it as the endpoint of a period of accelerating technological progress, where rates of change go infinite and (almost) the entire species either self-destructs or transcends ordinary existence.

It's important to look for current examples of looming singularities, or developments which could lead to them. What could cause sudden large-scale chaos? Besides technological breakthroughs, perhaps widespread and uncontrollable disease, or heightened tribalism, or cosmic disaster, or mass irrationality, or ....?